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Author : Grace Wahba
Release : 1973
Genre : Convergence
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Convergence Properties of the Method of Regularization for Noisy Linear Operator Equations by : Grace Wahba
Download or read book Convergence Properties of the Method of Regularization for Noisy Linear Operator Equations written by Grace Wahba. This book was released on 1973. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Grace Wahba
Release : 1973
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Convergence Properties of the Method of Regularization for Noisy Linear Operation Equations by : Grace Wahba
Download or read book Convergence Properties of the Method of Regularization for Noisy Linear Operation Equations written by Grace Wahba. This book was released on 1973. Available in PDF, EPUB and Kindle. Book excerpt: Convergence properties of the method of regulation for finding approximate solutions to the linear operator equation g = Kf are found when g is contaminated by noise. If f belongs to (H sub R), a reproducing kernel Hilbert Space and K((H sub R)) = (H sub Q), another r.k.h.s. which is topologically equivalent to W2(m), it is shown how the optimum choice of lambda depends on n, m, the mean square noise, and f. (Author).
Author : Willi Freeden
Release : 2023-08-21
Genre : Mathematics
Kind : eBook
Book Rating : 453/5 ( reviews)
Book Synopsis Recovery Methodologies: Regularization and Sampling by : Willi Freeden
Download or read book Recovery Methodologies: Regularization and Sampling written by Willi Freeden. This book was released on 2023-08-21. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to introduce the reader to methodologies in recovery problems for objects, such as functions and signals, from partial or indirect information. The recovery of objects from a set of data demands key solvers of inverse and sampling problems. Until recently, connections between the mathematical areas of inverse problems and sampling were rather tenuous. However, advances in several areas of mathematical research have revealed deep common threads between them, which proves that there is a serious need for a unifying description of the underlying mathematical ideas and concepts. Freeden and Nashed present an integrated approach to resolution methodologies from the perspective of both these areas. Researchers in sampling theory will benefit from learning about inverse problems and regularization methods, while specialists in inverse problems will gain a better understanding of the point of view of sampling concepts. This book requires some basic knowledge of functional analysis, Fourier theory, geometric number theory, constructive approximation, and special function theory. By avoiding extreme technicalities and elaborate proof techniques, it is an accessible resource for students and researchers not only from applied mathematics, but also from all branches of engineering and science.
Author : Anatoly B. Bakushinsky
Release : 2018-02-05
Genre : Mathematics
Kind : eBook
Book Rating : 383/5 ( reviews)
Book Synopsis Regularization Algorithms for Ill-Posed Problems by : Anatoly B. Bakushinsky
Download or read book Regularization Algorithms for Ill-Posed Problems written by Anatoly B. Bakushinsky. This book was released on 2018-02-05. Available in PDF, EPUB and Kindle. Book excerpt: This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems
Author : Thomas Schuster
Release : 2012-07-30
Genre : Mathematics
Kind : eBook
Book Rating : 723/5 ( reviews)
Book Synopsis Regularization Methods in Banach Spaces by : Thomas Schuster
Download or read book Regularization Methods in Banach Spaces written by Thomas Schuster. This book was released on 2012-07-30. Available in PDF, EPUB and Kindle. Book excerpt: Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.
